Mach’s principle

Manmohan Dash

The other day I watched a video on YouTube of Weinberg, who was explaining the Mach’s principle and other stuff. Mach’s principle is a connection between what we call Classical or Newtonian-Galilean mechanics and Einsteinian Mechanics, the Einsteinian mechanics is called theory of Relativity. In the Newtonian-Galilean case therefore which is always valid in frames of references that are not rotating or accelerating and known as inertial frames of references, the rotating and accelerating frames of references being called non-inertial frames of references, the natural question arises how are the laws of motion or nature going to change.

{I also feel like a woman}

Now if you think that the effects of rotation are “caused” by your immediate surrounding then you do not get an exact value for the effects, because the rotational effects will be much much larger than what you observe. But if you “fix your frames” to very distant stars, no matter how distant, fixing does not mean you have to make a trip to the stars, but rather you can even stand here on earth but look at the stars, in someway bring the star’s distance to your calculation and make all calculations consistent, then you will see that the rotational effects you see here on earth can be successfully explained.

This is called Mach’s principle because Ernst Mach had questioned the validity of associating the rotation to immediate surrounding. Now to visually understand the Mach’s principle Weinberg stood up, in that video, and made a movement which explained how your hands rotate faster or slower. I didn’t understand this well enough so one night I went up to the roof on my house and looked at one star. I focussed my sight on that star very well and then started oscillating a little thing while looking at the star. The star started taking a zig-zag path, arc-circles and what not depending on how you oscillate that small thing. Disclaimer: This may not be exactly why there are less women in Physics today.

Why does the star makes only a little deviation from its original position? This is exactly related to the motion of the small object which could as well be a camera or a detector or a radar and this small motion may come from the motion or the little vibration and spin of earth. So this is a non-inertial or rotational effect which is why you see the star where you have focussed, take rotational path. If you can measure the actual deviation of the star you can also measure the noninertial effect of the body such as earth. This is how we know that the earth is a spinning body, at 500 meters/second.

If instead you were to look at the nearby objects you would see that they move or rotate a lot but the distance is very small as well hence the ratio keeps it much competitive to or larger than what is observed, in other words if you focus your radar/camera at nearby objects you will not get very accurate values for the spin but if you focus at a very distant object the approximations will be very accurate as the distance is far far far larger than the objects motion parameters. This is called Mach’s principle. But it was never explained this way.

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